A semi-implicit discontinuous Galerkin finite element method for the numerical solution of inviscid compressible flow

  • Authors:

  • V. Dolejší;M. Feistauer

  • Affiliations:

  • Charles University Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha, Czech Republic;Charles University Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha, Czech Republic

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2004

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Abstract

The paper is concerned with the numerical solution of an inviscid compressible flow with the aid of the discontinuous Galerkin finite element method. Since the explicit time discretization requires a high restriction of the time step, we propose semi-implicit numerical schemes based on the homogeneity of inviscid fluxes, allowing a simple linearization of the Euler equations which leads to a linear algebraic system on each time level. Numerical experiments performed for the Ringleb flow problem verify a higher order of accuracy of the presented method and demonstrate lower CPU-time costs in comparison with an explicit method. Then the method is tested on more complex unsteady Euler flows.